Question

What is the amount of mass lost in grams, in order to result in an energy of $2\times {10}^6\text{kWh}$?

• A. $0.8g$
• B. $0.08g$
• C. $8g$
• D. $80g$

Answer 1

The correct option is B $0.08g$

Given:
Energy, $E=2\times {10}^{6}kWh$

$1kWh=3.6\times {10}^{6}J$

$⟹E=2\times {10}^6\times 3.6\times {10}^{6}J$

$⟹E=7.2\times {10}^{12}J$

According to Einstein's mass-energy equivalence, the lost mass $\Delta m$ can be converted into equivalent energy by the relation:
$E=\Delta m{c}^2$, where $c=3\times {10}^{8}m{s}^{-1}$ is the speed of light in vacuum.

Hence,
$\Delta m=\frac{E}{c^2}=\frac{7.2\times {10}^{12}}{(3\times {10}^8{)}^2}$
$=\frac{7.2\times {10}^{12}}{9\times {10}^{16}}$

$⟹\Delta m=0.8\times {10}^{-4}kg$

$⟹\Delta m=0.8\times {10}^{-4}\times {10}^{3}g$

$⟹\Delta m=0.8\times {10}^{-1}g=0.08g$